rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Integral Geometry and Valuations
  name:
    name part: Alesker, Semyon.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Fu, Joseph H.G.
    role:
      role term: author.
  name:
    name part: Gallego, Eduardo.
    role:
      role term: editor.
  name:
    name part: Solanes, Gil.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 112 p. online resource.
  abstract: Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces.
  table of contents: Part I: New Structures on Valuations and Applications -- Translation invariant valuations on convex sets -- Valuations on manifolds -- Part II: Algebraic Integral Geometry -- Classical integral geometry -- Curvature measures and the normal cycle -- Integral geometry of euclidean spaces via Alesker theory -- Valuations and integral geometry on isotropic manifolds -- Hermitian integral geometry.
  note: by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes.
  subject:
    topic: Mathematics
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Convex and Discrete Geometry
  subject:
    topic: Differential Geometry
  classification: QA639.5-640.7
  classification: QA640.7-640.77
  classification: 516.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Advanced Courses in Mathematics - CRM Barcelona
  identifier: 9783034808743
  identifier: http://dx.doi.org/10.1007/978-3-0348-0874-3
  record info:
    record creation date: 141009
    record change date: 20151103131436.0
    record identifier: 978-3-0348-0874-3